Generating novel views of a three-dimensional object based on a single two-dimensional image

ABSTRACT

Embodiments are directed towards providing a target view, from a target viewpoint, of a 3D object. A source image, from a source viewpoint and including a common portion of the object, is encoded in 2D data. An intermediate image that includes an intermediate view of the object is generated based on the data. The intermediate view is from the target viewpoint and includes the common portion of the object and a disoccluded portion of the object not visible in the source image. The intermediate image includes a common region and a disoccluded region corresponding to the disoccluded portion of the object. The disoccluded region is updated to include a visual representation of a prediction of the disoccluded portion of the object. The prediction is based on a trained image completion model. The target view is based on the common region and the updated disoccluded region of the intermediate image.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation of and claims priority to, U.S.patent application Ser. No. 15/433,731, filed on Feb. 15, 2017, entitledGENERATING NOVEL VIEWS OF A THREE-DIMENSIONAL OBJECT BASED ON A SINGLETWO-DIMENSIONAL IMAGE, the entirety of which is incorporated herein byreference.

BACKGROUND

Two-dimensional (2D) image sensors, such as cameras embedded in consumerelectronics, are now ubiquitous. As such, many users now enjoy readyaccess to digital photography. For instance, users often employ imagesensors to capture 2D image data of three-dimensional (3D) physicalobjects. A single 2D image provides a single view of a 3D object from asingle viewpoint, i.e. from the viewpoint of the image sensor. However,the user may desire another view of the 3D object from anotherviewpoint. Views of the object from other viewpoints traditionallyrequire additional images taken from multiple viewpoints. For instance,stereoscopic photography is one well-known method that enables a user toview a 3D object from multiple viewpoints. However, such methodstypically require data regarding the object beyond the data acquired viaa single 2D image sensor positioned at a single viewpoint.

SUMMARY

The present invention is directed towards providing a target or novelview of a 3D object. The target view is from a target (or novel)viewpoint. Various methods include receiving a source image thatincludes a source view of the object, generating an intermediate imagethat includes an intermediate view of the object, updating a disoccludedregion of the intermediate image, and providing the target view. Thesource image is encoded in 2D data. The source view is from a sourceviewpoint. Furthermore, the source view includes a common portion of theobject. The intermediate image is based on the 2D data. The intermediateview is from the target viewpoint and includes the common portion of theobject, as well as a disoccluded portion of the object. The disoccludedportion of the object is occluded (or not visible) in the source view.The intermediate image includes a common region corresponding to thecommon portion of the object. The intermediate image also includes adisoccluded region corresponding to the disoccluded portion of theobject.

The disoccluded region of the intermediate image is updated to includeat least a visual representation of a prediction of the disoccludedportion of the object. The prediction of the disoccluded portion of theobject is based on a trained image completion model. The target view ofthe object is based on the common region of the intermediate image, aswell as the updated disoccluded region of the intermediate image thatincludes the visual representation of the prediction of the disoccludedportion of the object.

Some methods further include generating a visibility map and determininga plurality of pixels included in the disoccluded region of theintermediate image based on the visibility map. The visibility map maybe based on the source image and a rotational transformation from thesource viewpoint to the target viewpoint.

At least one method includes generating a flow field that maps a commonregion of the source image to the common region of the intermediateimage, determining pixel values for each of the pixels included in thecommon region of the intermediate image based on the flow field, andgenerating the intermediate image based on the determined pixel valuesincluded in the common region of the intermediate image. The flow fieldmay be based on the rotational transformation from the source viewpointto the target viewpoint. The common region of the source imagecorresponds to the common portion of the object. Determining the pixelvalues may be further based on a sampling kernel and at least a portionof the 2D data that encodes the source image. The portion of the 2D datacorresponds to the common portion of the object.

Still other methods include determining a foreground region of thesource image, determining a foreground of the intermediate image, andgenerating a background map based on the intersection of the foregroundregion of the source image and the foreground region of the intermediateimage. The foreground region of the source image may correspond to theobject. The foreground region of the intermediate image may correspondto the object. The methods further include determining a backgroundregion of the intermediate image based on the background map anddetermining a pixel value for the pixels included in the backgroundregion of the intermediate image. The pixel values may be based on abackground region of the source image. The background region of thesource image is the compliment to the foreground region of the sourceimage.

Generating the intermediate image may be further based on a geometricflow model that determines a rotation of the object about an accessincluded in a plane of the 2D data. The geometric flow model may betrained to determine a boundary of the common region of the intermediateimage based on the 2D data that encodes the source image and therotational transformation from the source viewpoint to the targetviewpoint. Furthermore, the image completion model may be trained with acombination of an adversarial loss metric and a feature loss metric. Theadversarial loss metric discriminates between synthetic images andnatural images. The feature loss metric discriminates between physicalfeatures included in a plurality of images.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A illustrates an exemplary embodiment of a source image andmultiple exemplary embodiments of a novel target images generated by thevarious embodiments discussed herein.

FIG. 1B illustrates an image generation system implementing variousembodiments presented herein.

FIG. 2A illustrates an exemplary embodiment of a geometric flow networkemploying a geometric flow model that is consistent with the variousembodiments presented herein.

FIG. 2B illustrates an exemplary embodiment of a disocclusion-awaregeometric flow network that generates a visibility map and is consistentwith the various embodiments presented herein.

FIG. 2C shows various source images and ground-truth target images, aswell as visibility maps and intermediate images generated by the variousembodiments discussed herein.

FIG. 3A illustrates an exemplary embodiment of an image completionnetwork employing an image completion model that is consistent with thevarious embodiments presented herein.

FIG. 3B shows various incomplete intermediate images, target images, andground-truth target images, generated by the various embodimentsdiscussed herein.

FIG. 4 shows various source images, unmasked intermediate images,visibility maps, background maps, and target images generated by thevarious embodiments discussed herein.

FIG. 5 illustrates one embodiment of a process flow for generating anovel target image that is consistent with the various embodimentspresented herein.

FIG. 6A illustrates one embodiment of a process flow for generating anintermediate image that is consistent with the various embodimentspresented herein.

FIG. 6B illustrates one embodiment of a process flow for determiningpixel values for a disoccluded region of an intermediate image that isconsistent with the various embodiments presented herein.

FIG. 6C illustrates one embodiment of a process flow for determiningpixel values for a background region of an intermediate image that isconsistent with the various embodiments presented herein.

FIG. 7 illustrates one embodiment of a process flow for generating atarget image based on an intermediate image that is consistent with thevarious embodiments presented herein.

FIG. 8A illustrates one embodiment of a process flow for training animage completion system that is consistent with the various embodimentspresented herein.

FIG. 8B illustrates one embodiment of a process flow for training ageometric flow network that is consistent with the various embodimentspresented herein.

FIG. 8C illustrates one embodiment of a process flow for training animage completion network that is consistent with the various embodimentspresented herein.

FIG. 9 is a block diagram of an example computing device in whichembodiments of the present disclosure may be employed.

DETAILED DESCRIPTION

Briefly stated, various embodiments are directed towards generatingand/or synthesizing novel views of a three-dimension (3D) object basedon a single source (or input) image of the object. As used herein, theterm “viewpoint” may refer to orientation of the optical axis of aviewer of an image. Thus, the “source viewpoint” may refer to at leastan approximate position of an image sensor (e.g. a camera) that capturesthe source image. Likewise, the “target viewpoint” may refer to theposition of a virtual camera that may be employed to capture the targetimage. For instance, a target viewpoint may be the viewpoint at which itappears the target image is captured. A viewpoint may be referenced, viaspherical coordinates, such as the rotational orientation of thecamera:(θ, φ). Accordingly, the viewpoint of an image may refer to theorientation of a vector normal to the image and positioned at the centerof the image.

As used herein, the term “disoccluded portion of the object” is used toreference at least a portion of the portion of the object that is notvisible (i.e. occluded) from the source viewpoint, but is visible (i.e.disoccluded) from the target viewpoint. Accordingly, the disoccludedportion of the object is a portion of the object is visible from thetarget viewpoint, but, in response to a rotational transformation fromthe target viewpoint to the source viewpoint, becomes occluded (i.e. thedisoccluded portion is not visible from the source viewpoint).

As used herein, the term “common region” of an image may refer to theregion of the image that corresponds to the common portion (relative tothe source image) of the 3D object. Similarly, the “disoccluded region”of an image refers to the region of the image that corresponds to thedisoccluded portion of the 3D object (i.e. the portion of the objectthat is non-visible/occluded from the source viewpoint butvisible/disoccluded from the target viewpoint).

As used herein, the term “natural image” refers to an image where thepixel values are based directly on signals generated via one or moreimage sensors. In contrast, a “synthetic image” may include at leastregions of pixels, where the corresponding pixel values are not directlybased on signals generated via image sensors and/or cameras. Rather, thepixel values of a synthetic image may be predicted, determined,generated, hallucinated, deduced, or otherwise inferred from informationother than image sensor signals. As used herein, the term “weights” mayrefer to the connectivity weights between the connections of the nodesof the various machine-learning networks discussed.

As noted above, embodiments are directed towards generating views of the3D object based on a single source image of the object. The source imagemay be a two-dimensional (2D) image of the 3D object from a singlesource (or input) viewpoint. The various embodiments generate a target(or output) image of the object from a novel target (or output)viewpoint. Thus, the various embodiments provide a visual representationof a rotational transformation (corresponding to the transformation fromthe source viewpoint to the target viewpoint) of a 3D object based on 2Dsource data (from a single viewpoint) that lacks object informationcorresponding to the third spatial dimension. Furthermore, the 2D sourcedata lacks information corresponding to portions of the 3D object thatare occluded in the source viewpoint. The various embodimentshallucinate (or predict) the visual representation of such disoccludedportions of the 3D object and include the hallucination in the targetimage.

Previously available image generation or synthesis systems mainly employone of two image synthesis methodologies: (a) geometry-based viewsynthesis and (b) image synthesis networks. Some previously availablegeometry-based systems employ multiple source images that includemultiple views of the object (from multiple viewpoints.) For instance,stereoscopic photography techniques and techniques for interpolatingvisual information corresponding to a target viewpoint between themultiple input viewpoints have been employed in previous systems. Incontrast to such previous systems, the various embodiments herein employonly a single 2D image, from a single viewpoint, of the 3D object.

Other geometry-based previously available systems include otherlimitations. As discussed below, such systems may be limited in anability to hallucinate or predict portions of the object that areoccluded in the source image, but are disoccluded from the targetviewpoint. For instance, some geometry-based systems estimate a depthmap corresponding to the portion of the object that is visible in theinput image. Such systems generate a view of the object from a differentviewpoint via geometric transformations of the depth map. However,because such systems employ only a single image, they are limited in theability to hallucinate the disoccluded portion of the object.

Other geometry-based systems may employ collections of 3D models tohallucinate disoccluded portions of objects. For example, variousprevious systems first identify a type of object included in the inputimage. These systems may then access a 3D model for an object of anequivalent or similar object type. Such systems may have access to large3D model databases, or search the Internet for a 3D model. However, suchsystems are limited in the availability of 3D models for similar objecttypes. In contrast to these previous systems, the embodiments hereinonly rely on 3D models to train various machine-learning models, i.e.once trained, the various embodiments herein do not rely on 3D models totransform from the source viewpoint to the target viewpoint, or tohallucinate the disoccluded portions of the object.

Other previously available image synthesis systems have employed imagesynthesis networks to generate visual representations of previouslyunseen portions of objects. However, such image synthesis networks aretypically not enabled to generalize hallucinations for object types notpreviously seen. Such systems may hallucinate global structures includedin the object. However, the generated hallucinations may fail tohallucinate local structures included in the object or tend to includeartifacts, such as blurriness and aliasing.

In contrast to these previously available systems, the variousembodiments herein employ a plurality of trained image generationnetworks included in an automated image generation pipeline or workflow.The workflow receives a single 2D source image. The source image is froma source viewpoint. The workflow generates an intermediate image of theobject from a target viewpoint, via a geometric flow network that istrained to transform 2D visual information included in the source imageto a novel viewpoint. Unlike previous systems, the geometric flownetwork only requires a 3D model of the object during the training phaseof the network, i.e. once trained a geometric flow network does notrequire a 3D model of the object when employed to transform 2D visualinformation included in the source image to a novel viewpoint. Infurther contrast to previous systems, the pixels corresponding to thedisoccluded portion of the object (i.e. the portion of the object thatis non-visible/occluded from the source viewpoint butvisible/disoccluded from the target viewpoint) are masked in theintermediate image, via a visibility map. That is to say that thegeometric flow network may be a disocclusion-aware network.

Another network (an image completion network) hallucinates thedisoccluded portion of the object, within the intermediate image. Thus,the trained image completion network generates values for the maskedpixels of the intermediate image. A target image is generated based onthe intermediate image, including the hallucinated portion of theobject. The workflow further refines the target image by removingartifacts that may have been generated by the various networks. Asdiscussed below, another trained network (a loss network) may beemployed to adversarially train the other networks. The loss networkemploys a combination of adversarial, (global and local) feature, andpixel loss functions and/or models.

FIG. 1A illustrates an exemplary embodiment of a single 2D source image100 and multiple exemplary embodiments of novel target images 110generated by the various embodiments discussed herein.

In FIG. 1A, 2D source image 110 is from source viewpoint V_(S)={θ_(S),ϕ_(S)}. Each of the target images 110 is from a separate targetviewpoint. In particular, exemplary target image 112 is from targetviewpoint V_(T)={θ_(T), ϕ_(T)}. Rotational transformationR=V_(T)−V_(S)={Δθ, Δ℠}={θ_(T)−θ_(S), ϕ_(T)−ϕ_(S)}, is a rotationaltransformation from the source viewpoint to the target viewpoint.Although the 3D object illustrated in FIG. 1A is an automobile, itshould be understood that other embodiments are not so limited, and theobject may be an object of virtually any object type.

As shown in FIG. 1A, rotational transformation R may result in adisocclusion of a portion of the 3D object (and an occlusion of anotherportion of the 3D object). For instance, if the axis of the rotationaltransformation is at least partially within the plane of the sourceimage (i.e. the axis includes a component within the plane of the sourceimage), a portion of the object is not visible from the sourceviewpoint, but is visible from the target viewpoint.

For objects lacking symmetry along one or more axes of the rotationaltransformation, the 2D source image lacks information associated withthe disoccluded portion of the object (i.e. the portion of the objectthat is non-visible/occluded from the source viewpoint butvisible/disoccluded from the target viewpoint). For instance, the grillportion 144 (or the front end) of the automobile is occluded in sourceimage 110. However, the grill portion 114 is a disoccluded portion ofthe automobile because the grill portion is occluded in the source image110, but becomes visible/disoccluded in target image 112 due to therotational transformation from the source view to the target viewpoint.As also shown in FIG. 1A, the embodiments herein provide a visualrepresentation of the disoccluded (or previously occluded) portion ofthe object. More specifically, the embodiments hallucinate (or predict)the disoccluded portion of the object without requiring inputinformation corresponding to the disoccluded portion of the object.

Exemplary Image Generation System

FIG. 1B illustrates an image generation system (IGS) 150 implementingvarious embodiments presented herein. System 150 includes an imagegeneration computing device (IGCD) 158 and a user-computing device 156that are communicatively coupled via communication network 152. Otherembodiments of an IGS may include more or less computing devices. IGCD158 may be employed to generate novel target images, as discussed inconjunction with the various embodiments. For instance, in anon-limiting embodiment, a user may employ user-computing device 156 toremotely provide, via communication network 152, a source image, controlthe generation of the novel target images, and view the generated targetimages. IGCD 158 may provide, via communication network 152, the targetimage to the user, via user-computing device 156.

It should be noted that IGCD 158 and/or user-computing device 156 mayinclude virtually any computing device. For instance, at least one ofIGCD 158 and/or user-computing device 156 may be a server computingdevice, a client computing device, a laptop computing device, a desktopcomputing device, a mobile computing device, and the like. In otherembodiments, the functionality of each of IGCD 158 and user-computingdevice 156 may be implemented in a single computing device or acombination of multiple computing devices that includes additionalcomputing devices not shown in FIG. 1B.

System 150 also includes a training database 154 that is alsocommunicatively coupled to at least IGCD 158 and/or user-computingdevice 156, via communication network 152. Training database 154 mayinclude training data employed to train the various machine-learningnetworks discussed herein.

Communication network 152 may be any communication network, includingvirtually any wired and or wireless communication technologies, wiredand/or wireless communication protocols, and the like. It should beunderstood that communication network 152 may be virtually anycommunication network that communicatively couples a plurality ofcomputing devices and databases in such a way as to enable users ofcomputing devices to exchange information via the computing devices.

System 150 includes a plurality of machine-learning networks. In theembodiment shown in FIG. 1B, system 150 includes at least geometric flownetwork (GFN) 160, image completion network (ICN) 170, and loss network180. Alternative embodiments may include more or less machine-learningnetworks. IGCD 158 may host, implement, or otherwise include suchmachine-learning networks. For instance, in the non-limiting embodimentshown in FIG. 1B, IGCD 158 hosts GFN 160, ICN 170, and loss network 180.In alternative embodiments, user-computing device 156 may host suchmachine-learning networks.

GFN 160, ICN 170, and/or loss network 180 may be deep learning networks(or simply deep networks). At least one of GFN 160, ICN 170, and/or lossnetwork 180 may be an artificial neural network, such as a deep neuralnetwork. At least one of GFN 160 or ICN 170 may be an agent, such as ageneralized artificial intelligence (AI) agent. In various embodiments,more or less machine-learning/deep learning networks are hosted via IGCD158 and/or user-computing device 156. However, virtually any computingdevice that is communicatively coupled to training database 154 may beemployed to train, implement, and/or host such deep-learning networks.

GFN 160 may include similar features, components, and/or functionalityas GFN 200 of FIG. 2A and GFN 260 of FIG. 2B. However, briefly, GFN 160is trained to generate an intermediate image, from the target viewpoint,based on a transformation of a 2D source image, from the sourceviewpoint. Due to disocclusion of one or more portions the 3D object,the intermediate image is incomplete. The ICN 170 is trained to generatethe target image by generating a prediction (or hallucination) for theincomplete regions of the intermediate image. Loss network 180 may betrained and employed to trained the ICN 170 based on an adversarial lossmodel (or function) 182, the feature loss model (or function) 184, andthe pixel-loss function model 186. Loss network 180 may be anadversarial-trained network.

In various embodiments described herein, loss network 180 may employtraining data included in training database 154 to train ICN 170 and/orGFN 160. At least one of GFN 160 and/or ICN 170 may be aconvolutional/deconvolutional network. Accordingly, thesemachine-learning networks may include a plurality of convolution (orencoding) layers and/or a plurality of deconvolution (or decoding)layers.

As discussed throughout, the workflow of system 150 for generating atarget image from a novel target viewpoint includes receiving a 2Dsource image. FIG. 1B shows GFN 160 receiving a single 2D source image164. Source image 164 includes a view of the 3D object (an automobile)from the source viewpoint Vs. In various embodiments, source image 164is encoded via 2D data that lacks and/or does not include objectinformation in the third spatial dimension. Furthermore, source image164 is from a single viewpoint, i.e. the source viewpoint. GFN 160 doesnot require a 3D model of the object or image data of the object frommultiple viewpoints.

In addition to source image 164, GFN 160 may receive one or moreviewpoint parameters that indicate the target viewpoint V_(T)={θ_(T),ϕ_(T)}. For instance, the received viewpoint parameters may include oneor more of V_(T)={θ_(T), ϕ_(T)} and/or rotational transformationR=V_(T)−V_(S)={Δθ, Δϕ}={θ_(T)−θ_(S), ϕ_(T)−ϕ_(T)}. In at least oneembodiment, the one or more viewpoint parameters includes one or moreparameters indicating the source viewpoint, V_(S)={θ_(S), ϕ_(S)}.

Based on the 2D data encoding source image 164 and the one or moreviewpoint parameters, GFN 160 generates an intermediate image 174.Intermediate image 174 includes an intermediate view of the object fromthe target viewpoint. The intermediate view of the object is a rotatedview of the object, where the rotation is based on the rotationaltransformation.

A portion of the object is common to each of the views in source image164 and the intermediate image 174. The boundaries of this commonportion of the object are approximately demarcated via the hash marks192 in source image 164 and via hash marks 194 in intermediate image174. The GFN 174 is trained to rotationally transform (or rotate) thecommon region (indicated via hash marks 194) of intermediate image 174,relative to the common region (indicated via hash marks 192) of sourceimage 164, without requiring a 3D model (or other 3D data) of theobject.

More particularly and as discussed below, GFN 160 is trained to generatea flow field that maps regions (and thus pixel values) of source image164 to corresponding regions (and thus corresponding pixel values) ofthe intermediate image based on the rotational transformation R. Notethat source image 164 lacks 3D information regarding the object toassist with such a transformation. Rather, GFM 162 of GFN 160 is trainedto perform such a transformation without the 3D data normally employedto perform such a rotational transformation, e.g. by explicitlyrotationally transforming (or moving) pixel values via the flow field.

As also shown in FIG. 1B, the intermediate view of the object inintermediate image 174 includes a portion of the object that wasoccluded in the view of source image 164, but is disoccluded inintermediate view of intermediate image 174. The boundaries of thedisoccluded portion (or previously occluded portion) of the objected areapproximately demarcated via hash markings 196 in intermediate image174. Thus, intermediate image 174 includes a region corresponding to thecommon portion (indicated via hash markings 194) of the object andanother region corresponding to the disoccluded portion (indicated viahash markings 196) of the object.

Hash marks 194 approximately demarcate the boundaries of the commonregion of intermediate image 174. Likewise, hash marks 196 approximatelydemarcate the boundaries of the disoccluded region of intermediate image174.

Note that the intermediate image 174 is an incomplete image due to thedisocclusion of disoccluded portion 196. More specifically, the pixelsincluded in the disoccluded region of intermediate image 174 have beenmasked out, not included, or otherwise set to a single value. The 2Ddata encoding source image 192 does not include (or lacks) informationcorresponding to the disoccluded portion 196 (i.e. the portion of theobject that is non-visible/occluded from the source viewpoint butvisible/disoccluded from the target viewpoint). Accordingly, if theinformation included in the source 164 is employed to generate the pixelvalues within the disoccluded region of intermediate image 196, thedisoccluded region would be distorted.

In some embodiments, GFN 160 is a disocclusion-aware network. In suchembodiments, GFN 160/GFM 162 is trained to generate a visibility map.That is to say, GFN 160 is trained to detect and/or determine whichpixels in the intermediate image that correspond to the disoccludedportion of the object. That is to say, GFN 160 is a disocclusion-awareGFN that is enabled to determine the location pixels included in thedisoccluded region of the intermediate image. The visibility map isessentially a pixel mask that is employed to update the intermediateimage such that the pixel values included in the disoccluded regions arenot erroneously predicted via the flow field applied to the sourceimage. As shown in FIG. 1B, intermediate image 174 has been updated tomask out and/or not included pixels included in the disoccluded region.Thus, intermediate image 174 is an incomplete image.

The intermediate image 174 is provided to ICN 170 for image completion.Essentially, ICM 172 is trained to hallucinate (or predict) thedisoccluded region of intermediate image 174. Essentially, the ICM 172is trained to generate a prediction of the disoccluded portion of theobject and/or a prediction for the disoccluded region of theintermediate image 174. The ICM 172 updates the incomplete region ofintermediate image 174 with the prediction. As discussed herein, one ormore skip connections 166 from the GFN 160 to ICN 170 may be employed toprovide information, such as detected object features, from the variousencoding/decoding layers in GFN 160 to various encoding/decoding layersof ICN 170.

ICM 172 generates target image 190 based on intermediate image 174 andthe prediction of the disoccluded portion 198 of the object. Similar tointermediate image 174, target image 190 is from target viewpoint VT.Target image 190 includes a target view of the object that includes thecommon portion of the object (as rotated from the source viewpoint VsviaGFN 160), as well as a prediction (or hallucination) of the disoccludedportion of the object in the target image 190. More particularly, targetimage 190 includes the common portion of the intermediate image and aprediction for the disoccluded region of the intermediate image. Thus,ICN 170 may complete an incomplete intermediate image.

As discussed herein, additional skip connections from the encodinglayers of ICN 170 to the decoding layers of ICN 170 (not shown in FIG.1B) may be utilized to efficiently propagate information throughout ICN170. ICN 170 may be additionally trained to remove artifacts in targetimage 190 that are introduced via the generation of the intermediateview 174 and/or the target image 190.

Training data, included in training database 154, may be employed totrain one or more of these GFN 160, ICN 170, or loss network 180. Morespecifically, training data may be used to train a geometric flow model(GFM) 162 implemented via GFN 160 and an image completion model (ICM)172 implemented via ICN 170. Such machine-learning networks may betrained via back-propagation techniques that rely on ground-truth dataincluded in training database 154. Thus, in various embodiments, thetraining of at least one of GFN 160, ICN 170, or loss network 170includes supervised learning. As described below, loss network 180 mayimplement at least an adversarial loss model 182, a feature loss model184, and a pixel loss model 186 to train GFN 160 and/or ICN 170. Thetraining data may be employed to train adversarial loss model 182 andfeature loss model 184.

The adversarial loss model 182 may be trained to discriminate betweennatural images and synthesized images, i.e. generated images thatinclude pixel values not directly based on signals generated via imagesensors and/or cameras. Thus, adversarial loss model 182 may be aclassifier model. For instance, the adversarial loss model 182 may betrained to generate an adversarial loss metric that discriminatesbetween a natural image and a synthetic image.

As discussed above, ICN 170 may generate a complete image by predictingpixel values for incomplete regions of an incomplete image. The trainedadversarial loss model 182 generates an adversarial loss metric based onthe predicted pixel values. The adversarial loss metric indicates aprobabilistic metric for whether the completed image is a natural orsynthesized image. Adversarial loss model 182 may be trained viatraining data included in training database 154 of FIG. 1B. Forinstance, such training data may include a plurality of synthesizedimages and natural images.

Once trained, the adversarial loss model 182 and the GFM 162 may beemployed to train the ICN 170 in an adversarial mode. For instance, whentraining the ICN 170, the trained GFN 160 may generate an incompleteimage. The semi-trained ICN 170 may generate a complete image based onthe incomplete image. During training, the weights of the ICM 172 may beadjusted to complete an image that “tricks” or “fools” the adversarialloss model into misclassifying the completed image as a natural image.Thus, the ICN 170 is trained to generate more “natural” predictions ofthe disoccluded portion of the objects.

Feature loss model 184 may be further employed in the training of ICN170. For instance, each of the GFN 160 and ICN 170 may be trained torecognize various features in the objects. More specifically, thevarious convolutional layers in the networks may determine and/or detectobject features. The feature loss model 184 may be employed whentraining ICN 170 to conserve recognized features in the prediction ofthe disoccluded portion of the object. More particularly, the featureloss model 184 generates a feature loss metric that discriminatesbetween physical features included in an image.

The pixel loss model 186 may be employed to train the ICN 170. Forinstance, the pixel loss model 186 may generate a pixel loss metric thatindicates various pixel-wise differences between images. The pixel lossmetric may indicate pixel-wise comparisons of images, gradients ofimages, and the like. As discussed throughout, training the GFN 160and/or ICN 170 may include one or more linear and/or nonlinearcombinations of the trained adversarial loss model 182, the feature lossmodel 184, or the pixel loss model 186. The combinations may beparameterized via one or more hyperparameters.

Exemplary Geometric Flow Network

FIG. 2A illustrates an exemplary embodiment of a geometric flow network(GFN) 200 employing a geometric flow model (GFM) that is consistent withthe various embodiments presented herein. GFN 200 is machine-learningnetwork that is trained to generate an intermediate image based on asource image and one or more viewpoint parameters, such as but notlimited to rotational transformation R. GFM 200 may include similarfeatures, components, and/or functionality as GFN 160 of FIG. 1B.Training GFN 200 and/or a GFM (implemented via GFN 200) to generate anintermediate image is discussed in conjunction with at least process 820of FIG. 8B. GFN 200 may be deep neural network, where the weights of theconnections are trained via training data that includes ground-truthdata. Thus, the GFM may include the trained weights. Back-propagation ofone or more loss metrics may be employed to iteratively update theweights until training convergence.

GFN 200 includes a plurality of convolution (or encoding) layers 202 anda plurality of deconvolution (or decoding) layers 204. Convolutionlayers 202 may include image encoders and deconvolution layers 204 mayinclude image decoders. Thus, GFN 200 may be aconvolutional/deconvolutional (encoding/decoding) network. GFN 200 mayalso include one or more rotational layers 216. Note that the integermarkings shown in the convolution/deconvolution layers 202/204 showvalues for the filter size and bit depth at the various layers. Thevarious convolutional layers may be trained to detect and encode variousfeatures in an image. The various rotational layers 216 may be trainedto rotationally transform features encoded via the convolution layers204. The deconvolution layers 204 may be trained to reconstruct (ordecode) the features rotated via the rotational layers 216. GFN 200 alsoincludes one or more skip connections 218 to provide information animage completion network (now shown in FIG. 2A).

As shown in FIG. 2A, GFN 200 receives and/or is provided a source image210 that includes a view of a 3D object from a source viewpoint. GFN 200also receives and/or is provided a rotational transformation R (or otherviewpoint parameters). GFN 200 generates intermediate image 212. Morespecifically, GFN 200 generates a flow field 208 that maps pixellocations in source image 210 to corresponding pixel locations in thetarget image 212 based on R. As discussed throughout, GFN 200 may betrained to generate flow field 208 without requiring 3D data regardingthe object. A sampling kernel 206 is employed to determine the pixelvalues for intermediate image 212 based on flow field 208. In variousembodiments, the sampling kernel may be a bilinear sampling kernel. Forinstance, the pixel values (I_(l) ^(i,j)) for a pixel included inintermediate image 212 may be at least initially determined based on thegenerated flow filed (F) as,

$I_{I}^{i,j} = {\sum\limits_{{({h,w})} \in}{I_{s}^{h,w}{\max \left( {0,{1 - {{F_{y}^{i,j} - h}}}} \right)}{{\max \left( {0,{1 - {{F_{x}^{i,j} - w}}}} \right)}.}}}$

(i,j) are pixels indexes for the intermediate image and and F_(x) ^(i,j)and F_(y) ^(i,j) indicate the x and y coordinates of the intermediateimage, N denotes the 4-pixel neighborhood of (F_(x) ^(i,j), F_(y)^(i,j)), and I_(S) ^(h,w) are pixel values in the source image ((h,w)are pixel indexes in the source image). During training of GFN 200, thevarious convolution/deconvolution layers 202/204 may be trained toexplicitly move pixels in the source image (to be locations in theintermediate image) without requiring explicit information of the 3Dgeometry of the object. Thus, when trained, GFN 200 is enabled topredict how pixels in the source image are transformed when a viewtransforms from the source viewpoint to the target viewpoint.

Each of source image 210 and intermediate image 212 includes a commonportion of the object. Hash markings 220 approximately demarcate theboundaries of the common portion of the object in source image 210 andintermediate image 212. Thus, hash markings 220 approximately bound thepixels included in the common region of intermediate image 212. Note therotational transformation, generated via flow field 208 and samplingkernel 206 of the common region of intermediate image 212, as comparedto source image 210. The source image 210 includes another portion ofthe object (indicated via hash markings 224) that is occluded in thetarget viewpoint.

Intermediate image 212 includes a disoccluded portion of the object (aportion of the object that was occluded in the source image 220) butdisoccluded from the target viewpoint. Hash markings 222 approximatelydemarcate the boundary for the pixels included in the disoccludedportion of intermediate image 212.

FIG. 2A also shows a ground-truth target image 214, i.e. the “true”image of the object from the target viewpoint. The ground-truth image214 includes the common portion (indicated hash markings 222) and thedisoccluded portion (via hash markings 226) of the object. Becausesource image 210 does not include the 3D information regarding thedisoccluded portion of the object (i.e. the portion of the object thatis non-visible/occluded from the source viewpoint butvisible/disoccluded from the target viewpoint), the disoccluded regionof the intermediate image 212 is distorted, as compared to thedisoccluded regions of the ground-truth image 214. Thus, in variousembodiments, GFN 200 may be trained as a disocclusion-aware network thatgenerates a visibility map to mask off such distorted (or erroneous)pixels.

FIG. 2B illustrates an exemplary embodiment of a disocclusion-aware GFN250 that generates a visibility map 264 and is consistent with thevarious embodiments presented herein. Various embodiments of training adisocclusion-award GFN are discussed in conjunction with at leastprocess 820 of FIG. 8B. Disocclusion-aware GFN 250 may be a deepconvolution/deconvolution neural network, where the GFM includes thetrained weights. Disocclusion-aware GFN 250 may include similarfeatures, components, and/or functionality as GFN 160 of FIG. 1B and GFN200 of FIG. 2A. For instance, disocclusion-aware GFN 250 includes aplurality of convolution layers 252, rotational layers 266, anddeconvolution layers 254. In addition to predicating a pixel thetransformation/rotation/movement of pixels in the source image to theintermediate image, disocclusion-aware GFN 250 is trained to predictand/or determine the location of pixels included in a disocclusionregion of an intermediate image. Furthermore, the disocclusion-aware GFN250 masks out, or explicitly does not include, such disoccluded pixelsin the intermediate pixels.

Disocclusion-aware GFN 250 receives a source image 260 (from a sourceviewpoint) and one or more viewpoint parameters, such as but not limitedto rotational transformation R. Disocclusion-aware GFN 250 generatesintermediate image 262, as discussed in conjunction of GFN 200 of FIG.2A. Similar to intermediate image 212 of FIG. 2A, intermediate image 262of FIG. 2B includes a disoccluded region (indicated via the box 272)that is distorted due to lack of information in the 2D source image 260.

Disocclusion-aware GFN 250 is trained to generate a visibility map 264.Visibility map 264 may be a binary image with a binary view of thecommon portion of the object from the target viewpoint. Moreparticularly, pixels associated with the common portion of the object(or common region of the intermediate image 262) may be set to a firstvalue and pixels associated with the disoccluded portion of the object(or the disoccluded region of intermediate regions 262) are set toanother value. For instance, as shown in FIG. 2B, pixels associated withthe common portion of the object in visibility map 164 are set to “1”(or “white”) and pixels associated with the disoccluded portion are setto “0” (or “black”). Thus, a masking operation (pixel-wise ANDoperation) may be performed to mask off (and/or zero-out) the pixelvalues for pixels included in the disocclusion region of intermediateimage 262.

In the various embodiments, a GFN, such as but not limited todisocclusion-aware GFN 250 may include one or more skip connections thatfeed forward information to an ICN, such as but not limited to ICN 200of FIG. 3A. FIG. 2B shows one non-limiting embodiment of such a skipconnection: skip connection 268. Note that disocclusion-aware GFN 250may include additional skip connections not shown in FIG. 2B.

Skip connection 268 be equivalent to, feed into, input into, or otherotherwise be provided to ICN 300, of FIG. 3A, via skip connection 320.Such skip connections may couple, or concatenate, mid-level convolutionlayers in a GFN to middle convolution layers in a ICN. Such skips layersmay provide information regarding detected features of the object to theICN. Providing information, to an ICN, regarding the object featuresdetected a GFN may be important because pixels associated with thefeatures are masked from the intermediate view, via the visibility map.That is to say, the ICN does not have access to the information thatencodes such features. For instance, various high-level object features(colors, edges, corners, macro-structures, and the like) may be detectedvia convolution layers in a GFN. The one or more skip connections mayprovide such detected features to the convolution layers of the ICN.Thus, the ICN may employ information provided via the skip connectionsto preserve such features when generating a prediction for thedisoccluded portion of the object.

As shown in FIG. 2B, pixels associated with the background region of theimage are also set to the value of the disoccluded pixels. Essentially,visibility map 264 may be a mask employed to update intermediate image262. Upon such a masking operation, updated intermediate image 266 isgenerated such that the disoccluded portion of the object is notincluded (and/or masked out) in updated intermediate image 266. Variousembodiments for generating a visibility map are discussed in conjunctionwith at least process 620 of FIG. 6B.

FIG. 2C shows various embodiments of source images and ground-truthtarget images, as well as visibility maps, intermediate images, andupdated intermediate images generated by the various embodimentsdiscussed herein. The intermediate images, visibility maps, and updatedintermediate images may be generated by a disocclusion-aware GFN, suchas but not limited to GFN 250 of FIG. 2B. Note that the disoccludedregion of the intermediate images is indicated via the box in theintermediate image column. The updated intermediate images have beenupdated via viability map applied as a mask to the correspondingintermediate image. The ground-truth images may be employed in trainingthe GFM and/or the GFN.

Exemplary Image Completion Network

FIG. 3A illustrates an exemplary embodiment of an image completionnetwork (ICN) 300 employing an image completion model (ICM) that isconsistent with the various embodiments presented herein. ICN 300 ismachine-learning network that is trained to predict (or hallucinate) atleast a visual representation of a disoccluded portion of an objectbased on an incomplete image, such as but not limited to an intermediateimage generated via a trained GFN. ICN 300 may be additionally trainedto generate a target image based on the prediction of the disoccludedportion of the object and the intermediate image. Thus, ICN network maybe trained to complete an incomplete intermediate image, such as but notlimited intermediate image 174 of FIG. 1B. Adversarially training ICN300 and/or an ICM to complete an intermediate image is discussed inconjunction with at least process 860 of FIG. 8C. The ICM may includethe trained weights.

Similar to GFN 200 and disocclusion-aware GFN 250 of FIGS. 2A and 2Brespectively, ICN 300 may be machine-learning network, where the weightsof the connections are trained via training data. ICN 300 includes aplurality of convolution (or encoding) layers 302 and a plurality ofdeconvolution (or decoding) layers 304. Thus, ICN 300 may be aconvolutional/deconvolutional network. ICN 300 also includes one or moreskip connections 318 between the convolution layers 302 and thedeconvolution layers 304. Another skip connection 320 may provideinformation from a GFN, such as but not limited to GFN 160 of FIG. 1B,GFN 200 of FIG. 2A, or GFN 250 of FIG. 2B. ICN 300 receives anintermediate image 310 from a GFN. For instance, skip connections suchas but not limited to skip connections 218 and 268 may be equivalent to,feed into, input into, or otherwise be provided to ICN 300 via skipconnection 320.

The intermediate image 310 is from the target viewpoint. GFN 300generates a target image 312 from the target viewpoint. The target image312 includes the common portion of the object (included in incompleteintermediate image 310), as well as the prediction for the disoccludedportion (not included in incomplete intermediate image 310).

FIG. 3B shows various incomplete intermediate images, target images, andground-truth target images, generated by the various embodimentsdiscussed herein. For instance, the intermediate images are incompleteintermediate images and may be generated via a disocclusion-aware GFN,such as but not limited to disocclusion-aware GFN 250 of FIG. 2B. Thetarget images may be generated by an ICN, such as but not limited to ICN300 of FIG. 3A. The ground-truth target images may be employed to trainthe GFN and/or the ICN.

FIG. 4 shows various source images, unmasked intermediate images,visibility maps, background maps, and target images generated by thevarious embodiments discussed herein. The unmasked intermediate images,visibility maps, and the background maps may be generated by one of thevarious embodiments of a GFN as discussed herein. The correspondingvisibility map and background map have not been applied to the unmaskedintermediate images. The target images may have been generated by one ofthe various embodiments of an ICN as discussed herein. Upon updating theunmasked intermediate images by masking the various regions of theintermediate image via visibility maps and background maps, an ICN maycomplete the incomplete intermediate image to generate the target image.

Generalized Processes for Generating Novel Views of Three-DimensionalObjects

Processes 500-860 of FIGS. 5-8C will now be discussed. Briefly,processes 500-860 may be employed to generate novel views of 3D objects,as discussed in conjunction with the various embodiments herein. Suchprocesses may be implemented, executed, or otherwise performed via asingle and/or a combination of computing devices, such as but notlimited to user-computing device 156 of FIG. 1B, IGCD 158 of FIG. 1B, orcomputing device 900 of FIG. 9.

FIG. 5 illustrates one embodiment of a process flow for generating anovel target image that is consistent with the various embodimentspresented herein. The target image may include a target view of a 3Dobject. The target image is from a target viewpoint. Process 500 beginsafter a start block, at block 502, where a source image is received. Thesource image may be received by virtually any means, including but notlimited to via a communication network. For instance, FIG. 1B showssource image 164 being received via communication network 152. Thesource image may include a source view of the object. In variousembodiments, the source image is encoded in 2D data. The source view isfrom a source viewpoint and includes a common portion of the object. Atblock 504, one or more target viewpoint parameters are received. The oneor more target viewpoint parameters may indicate a target viewpoint. Forinstance, the target viewpoint parameters may include target viewpointVs and/or a rotational transformation R.

At block 506, an intermediate image is generated. Various embodimentsfor generating an intermediate image are discussed in conjunction withat least process 600 of FIG. 6A. However, briefly here, the intermediateimage may be based on the received source image and the one or moreviewpoint parameters. More specifically, the intermediate image may bebased on the 2D data that encodes the source image. The intermediateimage includes an intermediate view of the object that is from thetarget viewpoint. The intermediate view includes the common portion ofthe object, as well as a disoccluded portion of the object that isoccluded in the source view of the object. The intermediate imageincludes a common region corresponding to the common portion of theobject and a disoccluded region corresponding to the disoccluded portionof the object. In at least one embodiment, the intermediate image is anincomplete image because the pixels included in the disoccluded regionhave been masked via a visibility map.

The intermediate image may be generated via a trained generation flownetwork (GFN) and/or a trained geometric flow network (GFM). Forinstance, FIG. 1B shows intermediate image 174 generated via GFN 160.Intermediate image 174 is an incomplete intermediate image that includesa common region (indicate via hash marks 194) and disoccluded region(indicated via hash mark 196). The pixels included in the disoccludedregion have been masked via a visibility map generated by GFN 160. TheGFM may be a disocclusion-aware GFN trained to generate the visibilitymap.

At block 508, a prediction for the disoccluded region of theintermediate image is generated. Various embodiments for generating aprediction for a disoccluded region are discussed in conjunction with atleast process 700 of FIG. 7. However, briefly, the incompleteintermediate image may be completed to include a prediction for themasked off disoccluded region. The intermediate image may be updated toinclude the prediction for the disoccluded region. The predictions forthe disoccluded region may be generated via a trained image completionnetwork (ICN) and/or an image completion model (ICM).

At block 510, a target image is generated. Various embodiments forgenerating a prediction for a disoccluded region are discussed inconjunction with at least process 700 of FIG. 7. However, briefly here,the target image is based on the intermediate image, as well as theprediction for the disoccluded region of the intermediate image. Assuch, the target image is from the target viewpoint. More particularly,the target image includes the common region of the intermediate imageand the prediction for the disoccluded region of the intermediate image.

FIG. 1B shows target image 190 that is generated via ICN 170. The targetimage 190 includes the common region of the intermediate image indicatedvia hash marks 194 and the prediction for the disoccluded region of theintermediate image indicated via hash marks 198. Thus, a trained ICN/ICMmay complete an incomplete intermediate image. At block 512, the targetimage is provided. The target image may be provided to a user byvirtually any means, including but not limited to a communicationnetwork. In at least one embodiment, the target image is displayed on adisplay device of a computing device, such as but not limited touser-computing device 156 and/or IGCD 158 of FIG. 1B. Process 500 mayterminate and/or return a calling process.

FIG. 6A illustrates one embodiment of a process flow for generating anintermediate image that is consistent with the various embodimentspresented herein. Process 600 begins, after a start block, at block 602where a GFM is trained. In various embodiments, training a GFM mayinclude training a GFN that implements the GFM. Various embodiments fortraining a GFM and/or GFN are discussed in conjunction with at leastprocess 820 of FIG. 8B. As discussed throughout, the GFN may be adisocclusion-aware GFN. Similarly, the GFM may be a disocclusion-awareGFM.

At block 604, a flow field is generated based on the generated/trainedGFM, a source image, and one or more target viewpoint parameters. In thevarious embodiments, the flow field maps regions of the source imagethat correspond to the object to corresponding regions of anintermediate image based on a rotational transformation indicated by theone or more target viewpoint parameters. The trained GFN and/or GFM maygenerate the flow field. For instance, FIG. 2A shows flow field 208, asgenerated via GFN 200.

At block 606, pixel values for pixels included in at least the commonregion of the intermediate image are determined based on the flow field,a kernel, and the source image. The kernel may be a bilinear samplingkernel. In some embodiments, the pixel values for the pixels included inthe disoccluded region of the intermediate image are also determined atblock 606. Because the flow field maps regions of the source image tocorresponding regions of the intermediate image, determining the pixelvalues for the intermediate image may be based on the 2D data (i.e.source image pixel values) encoding the corresponding regions of thesource image.

At block 608, a visibility map is generated. The visibility map may bebased on the GFM, the source image, and the one or more target viewpointparameters. Various embodiments for generating a visibility map arediscussed in conjunction with at least process 620 of FIG. 6B. However,briefly here, a disocclusion-aware GFN may generate the visibility map.For instance, FIG. 2B shows disocclusion-aware GFN 250 generatingvisibility map 264.

At block 610, pixel values for the disoccluded region of theintermediate image are determined based on the visibility map. Forinstance, the visibility map may be employed as a mask. Variousembodiments for determining pixel values for the disoccluded region ofthe intermediate image are discussed in conjunction with at leastprocess 620 of FIG. 6B. FIG. 2B shows determined pixel values for adisoccluded region of intermediate image 266, i.e. the pixel values areset to a single value indicating black in intermediate image 266.

As shown in FIG. 2A, the disoccluded region (indicated via hash marks222) of intermediate image 212 is distorted. To avoid such distortionwithin the intermediate image, the visibility map may be employed as amask to mask off pixels corresponding to the disoccluded portion of theobject within the intermediate image. That is to say, pixels included inthe disoccluded region of the intermediate image are set to a singlevalue (“0” corresponding to black), such that the intermediate image isan incomplete image (e.g. intermediate image 266). In other embodiments,the pixels included in the disoccluded region may be set to “0”corresponding to white—as shown in intermediate image 174 of FIG. 1B.

At block 612, a background map is generated. The background map may bebased on the GFM, the source image, and the one or more target viewpointparameters. Various embodiments for generating a background map arediscussed in conjunction with at least process 640 of FIG. 6C. However,briefly here, a background map may be a background mask. For instance,FIG. 4 shows various background masks generated by a trained GFN.

At block 614, pixel values for the background region of the intermediateimage are determined based on the background map and the source mask.Various embodiments for determining pixel values for the backgroundregion of the intermediate image are discussed in conjunction with atleast process 640 of FIG. 6C. However, briefly here, a pixel value foreach of the pixels included in the background region of the intermediateimage may be determined based on the background region of the sourceimage and the background map. At block 616, the intermediate image maybe determined based on the various determined pixel values. Forinstance, FIG. 2C shows various embodiments of intermediate imagesgenerated by processes consistent with process 600. Process 600 mayterminate and/or return a calling process.

FIG. 6B illustrates one embodiment of a process flow for determiningpixel values for a disoccluded region of an intermediate image that isconsistent with the various embodiments presented herein. Process 620begins, after a start block, where a viewpoint vector is determined. Theviewpoint vector is based on the one or more viewpoint parameters. Theviewpoint vector may be a vector pointing from the target viewpoint toan origin of the coordinate system that is used to define the sourceviewpoint and the target viewpoint. In at least one embodiment, theviewpoint vector is a vector pointing from the “center of the camera”observing the target viewpoint. The viewpoint vector may be referencedas {right arrow over (c)} ∈

³.

At block 624, source 3D coordinates of the object are determined basedon the GFM and the source image. The source 3D coordinates are the 3Dspatial coordinates for each pixel corresponding to the portions of theobject that are visible in the source image. The GFN is trained todetermine the source 3D coordinates. The source 3D coordinates may bereferenced as {right arrow over (x)}_(S) ^((i,j) ∈)

⁴, where (i,j) are pixel indexes for the source image.

At block 626, the target 3D coordinates of the object are determinedbased on the source 3D coordinates and the one or more target viewpointparameters. The target 3D coordinates are the 3D spatial coordinates forpixels corresponding to the object from the target viewpoint. In atleast some embodiments, to determine the target 3D coordinates, therotational transformation R is applied to the source 3D coordinates forpixels in the source image corresponding to the object. A perspectiveprojection (P) from the viewpoint is then performed on the rotatedcoordinates to determine the target 3D coordinates.

At block 628, the target normal vectors of object are determined basedon the target 3D coordinates of object. The target normal vectors may bethe surface normal vectors of the object from the target viewpoint. Atblock 630, the visibility map is determined based on the target normalvectors of object and the viewpoint vector. Basically, at block 630, thedot product between each of the target normal vectors and the viewpointvector is determined. If the dot product is positive, the point on thesurface is pointing toward the surface (and is thus visible).Accordingly, the corresponding pixel in the visibility map is set to 1.Otherwise, the corresponding pixel value is set to 0. The visibility mapmay be represented as M_(vis) ∈ [0,1]^(H×W) . The visibility map maygenerated via:

$M^{{({{{PR}{(\theta)}}{\overset{\rightarrow}{x}}_{s}^{({i,j})}})}^{h},{({{{PR}{(\theta)}}{\overset{\rightarrow}{x}}_{s}^{({i,j})}})}^{w}} = \left\{ {\begin{matrix}{{1\mspace{14mu} {if}\mspace{14mu} {\overset{\rightarrow}{c}}^{T}{R(\theta)}{\overset{\rightarrow}{n}}_{s}^{({i,j})}} > 0} \\{0\mspace{14mu} {otherwise}}\end{matrix}.} \right.$

{right arrow over (n)}_(S) ^((i,j)) represents the surface normalvectors for pixel (i,j) in the source image. The superscripts (h,w)represent pixel indexes in the visibility map. R(θ) ∈

^(3×4) represents a rotation matrix based on the target viewpointparameters and P ∈

^(3×3) is perspective projection matrix.

At block 632, the disoccluded region of the intermediate image isdetermined based on the visibility map M_(vis). At block 634, the commonregion of the intermediate image is determined based on the visibilitymap M_(vis). At block 636, the pixels values for the disoccluded regionof the intermediate image are updated. Blocks 632, 634, 636 may includeemploying the visibility map as a mask on the intermediate image.Accordingly, the intermediate image (I) may be updated via blocks 632,634, and 636 as:

I=I⊙M_(vis).

The operator ⊙ is a pixel-wise AND operator. Process 620 may terminateand/or return a calling process.

FIG. 6C illustrates one embodiment of a process flow for determiningpixel values for a background region of an intermediate image that isconsistent with the various embodiments presented herein. Process 640begins, after a start block, at block 642 where the foreground region ofthe source image is determined. The foreground region of the sourceimage may include each of the pixels corresponding to the object in thesource image. For instance, the trained GFN may be trained to determineforeground and background regions of a source image. At block 644, theforeground region of the intermediate image is determined. Similar tothe foreground region of the source image, the foreground region of theintermediate image may include each of the pixels corresponding to theobject in the intermediate image.

At block 646, a background map is generated based on the intersection ofthe foreground region of the source image and the foreground region ofthe intermediate image. The background map may be a background mask thatmasks away the background region of the intermediate image. Forinstance, FIG. 4 shows various embodiments of background maps generatedby a trained background-aware GFN. In one embodiment, the map may berepresented as

M_(BG) ^(i,j)=[B_(S) ^(i,j)∩B_(I) ^(i,j)]

B_(S) ^(i,j) is a background mask for the source image (generated viablock 642) and B_(I) ^(i,j) is a background mask for the intermediateimage (generated via block 644).

At block 648 the background region of the intermediate image isdetermined based on the background map. For instance, the background mapmay be used as a mask to mask off the background region of theintermediate image. At block 650 the pixel values for the backgroundregion of the intermediate image are determined based on the backgroundregion of the source image. Accordingly, the intermediate image (I) maybe updated via

I=I⊙M_(BG).

Process 640 may terminate and/or return a calling process.

FIG. 7 illustrates one embodiment of a process flow for generating atarget image based on an intermediate image that is consistent with thevarious embodiments presented herein. Process 700 begins, after a startblock, at block 702 where an ICM is trained. In various embodiments,training a ICM may include training a ICN that implements the ICM.Various embodiments for training a ICM and/or a ICN are discussed inconjunction with at least process 800 of FIG. 8A.

At block 704, an intermediate image is provided to an ICN thatimplements the trained ICM. For instance, FIG. 3A shows intermediateimage 310 being provided to ICN 300. As discussed in conjunction with atleast FIG. 3A, the intermediate image 310 may include a common regionand a disoccluded region. As shown in FIG. 3A, the disoccluded regionmay be incomplete because the GFN that generated intermediate image 310is a disocclusion-aware GFN. Essentially, such disocclusion-aware GFNgenerates a visibility map that is employed to mask off pixels includedin the disocclusion region. Thus, the intermediate image may be anincomplete image.

At block 706, a prediction for the disoccluded region of theintermediate image is generated based on the ICM. As discussedthroughout, the ICN is trained to generate such predictions. At block708, a target image is generated based on the intermediate image and theprediction for the disoccluded region. More specifically, the targetimage includes the common region of the intermediate image and theprediction for the disoccluded region of the intermediate image. Thus,the ICN is trained to complete incomplete intermediate images. At block710, artifact regions within the target image are detected. At block712, the ICN updates the artifact regions of the target image. Process700 may terminate and/or return a calling process.

FIG. 8A illustrates one embodiment of a process flow for training animage completion system that is consistent with the various embodimentspresented herein. Various embodiments of training an image completionsystem, such as but not limited to image completion system 150 of FIG.1B, may include training one or more GFNs and/or one or more INCs, suchas but not limited to GFN 160 and ICN 170. In at least one embodiment,training an image completion system may include training, or at leastemploying, one or more loss networks, such as but not limited to lossnetwork 180.

Process 800 begins after a start block, at block 802, where trainingdata is received. For instance, training data may be received via atraining database, such as but not limited to training database 154 ofFIG. 1B. The training data may include a plurality of 3D models. The 3Dmodels may be models of various 3D training objects. Because thetraining data includes 3D models, the training data may be a 3D dataset.

At block 804, the GFN is trained based on the training data. Variousembodiments of training a GFN are discussed in conjunction with at leastprocess 820 of FIG. 8B. However, briefly here, training a GFN mayinclude training a GFM to generate an intermediate image based on asource image, as discussed herein. The GFN may be a disocclusion-awareGFN. Thus, the GFN may be trained to generate visibility maps andbackground maps to generate an incomplete intermediate image.

At block 806, the ICN is trained based on the training data and thetrained GFN. In various embodiments, the training of the ICN may befurther based on a loss network, such as but not limited to lossnetworks 180 of FIG. 1B. Various embodiments of training an ICN arediscussed in conjunction with at least process 860 of FIG. 8C. However,briefly here, training an ICN may include training an ICM to generate atarget image based on the incomplete intermediate image. Thus, the ICMmay be trained to generate a predication for a di socclusion region ofthe incomplete intermediate image.

At block 808, the training of the GFN and the ICN may be iterativelyupdated based on the training data and the loss network. Output from theat least partially trained GFN may be employed as a feedback signal toiteratively update that training of the at least partially trained ICN.Likewise, output from the at least partially trained ICN may be employedas a feedback signal to iteratively update the training of the at leastpartially trained GFN. When the training of each of these networks hassatisfactorily converged, process 800 may terminate and/or return acalling process.

FIG. 8B illustrates one embodiment of a process flow for training a GFNthat is consistent with the various embodiments presented herein. Asdiscussed below, training a GFN may include supervised learningtechniques. Process 820 begins after a start block, at block 822, wherethe GFM is initialized. Initializing the GFM may include initializingthe weights of the GFM. At block 824, a 3D model from the training datais selected. The 3D model may be of virtually any object type, such asbut not limited to an automobile, a chair, or any other 3D object. The3D object may be a training object. At block 826, one or more trainingviewpoint parameters are selected. Training viewpoint parameters atblock 826 may include one or more parameters that indicate a trainingsource viewpoint and a training target viewpoint.

At block 828, a source image is generated. The source image may be atraining source image of the object of the 3D model, from the trainingsource viewpoint. The source image is based on the selected 3D model andthe training viewpoint parameters. For instance, a source image of the3D object from the training source viewpoint may be generated via the 3Dmodel. Thus, the source image at block 828 may include a view of thetraining object from the training source viewpoint. The view of thetraining object may include a common portion of the training object.

At block 830, a ground-truth flow field is generated. The ground-truthflow field is based on the selected 3D model, the source image, and thetraining viewpoint parameters that indicate at least the training targetviewpoint. At block 832, a ground-truth visibility map is generated. Theground-truth visibility map may be based on the selected 3D model, thesource image, and the training viewpoint parameters.

At block 834, a predicted flow field is generated. The predicted flowfield may be based on the GFM, the source image, and the trainingviewpoint parameters. At block, 836 a predicted visibility map isgenerated. The predicted visibility map may be based on the GFM, thesource image, and the training viewpoint parameters.

At block 838, a flow loss metric is determined. The flow loss metric maybe based on a flow loss model (or function) and a comparison between theground-truth flow field and the predicted flow field. At block 840, avisibility loss metric may be determined. The visibility loss metric maybe based on a visibility loss model (or function) and a comparisonbetween the ground-truth visibility map in the predicted visibility map.The flow loss metric and the visibility loss metric may be employed, viaback propagation, to train the geometric flow network.

At block 842, the GFM is updated based on the back propagated flow lossmetric and the visibility loss metric. Updating the GFM may includeupdating and/or adjusting the weights of the GFM. Various embodiments ofgradient descent, gradient ascent, or other methods for adjusting theweights of a machine-learning network may be employed to update the GFM.

At decision block 844, it is determined whether to select other trainingviewpoints. For instance, the GFM may be trained via other sourceviewpoints and/or other target viewpoints of the same 3D object. Ifother training source and/or target viewpoints are to be employed in thetraining of the GFM, process 820 returns to block 826 to select othertraining viewpoint parameters. Otherwise, process 820 flows to decisionblock 846.

At decision block 846, it is determined whether to select another 3Dmodel. For instance, another 3D model of another object type may be usedto further train the GFM. If another 3D model is to be selected, process820 returns to block 824. Otherwise process 820 may terminate and/orreturn a calling process.

FIG. 8C illustrates one embodiment of a process flow for training an ICNthat is consistent with the various embodiments presented herein. Asdiscussed below, training an ICN may include supervised learningtechniques. Process 860 begins after a start block, at block 862, wherethe ICM is initialized. Initializing the ICM may include initializingthe weights of the ICM. At block 864, a 3D model from the training datais selected. The 3D model may be of virtually any object type. The 3Dobject may be a training object. At block 866, one or more trainingviewpoint parameters are selected. Training viewpoint parameters atblock 866 may include one or more parameters that indicate a trainingsource viewpoint and a training target viewpoint.

At block 868, a source image is generated. The source image may be atraining source image of the object of the 3D model, from the trainingsource viewpoint. The source image is based on the selected 3D model andthe training viewpoint parameters. For instance, a source image of the3D object from the training source viewpoint may be generated via the 3Dmodel. Thus, the source image at block 868 may include a view of thetraining object from the source viewpoint. The view of the trainingobject may include a common portion of the training object.

At block 868, a ground-truth target image is also generated. Theground-truth target image is based on the 3D model and the trainingviewpoint parameters. The ground-truth target image includes aground-truth view of the selected training object from the trainingtarget viewpoint. The ground-truth view of the training object includesthe common portion of the training object and a disoccluded portion ofthe training object that was occluded in the view of the source image.The common portion of the object is rotated relative to the commonportion included in the view of the source image.

At block 870, a training intermediate image may be generated. Thetraining intermediate image may be based on the source image, theselected viewpoint parameters, and the trained geometric flow model. Forinstance, an at least partially trained GFM may be employed to generatethe training intermediate image based on the source image and thetraining target viewpoint. As discussed throughout, the trainingintermediate image may include a rotated view of the training objectthat is from the training target viewpoint. The rotated view of thetraining object includes a rotation of the common portion of thetraining object (relative to the view of the source image), as well asthe disoccluded portion of the training object.

As noted throughout, the training intermediate image may be anincomplete image due to the disocclusion of the disoccluded portion ofthe object. As discussed, the GFM may employ a viability map to mask offpixels corresponding to the disoccluded portion of the object.Furthermore, the training intermediate image is a 2D image.

At block 872, a predicted target image is generated. The predictedtarget image is based on the training intermediate image and the ICM.More particularly, the ICM is employed to generate a predicted image ofthe disoccluded portion of the training object. The predicted targetimage may be a predicted complete version of the incomplete trainingintermediate image. That is to say, the predicted target image mayinclude the rotated common portion of the object as well as thepredicted disocclusion portion of the object.

At block 874, an adversarial loss metric is determined based on anadversarial loss model (or function). More specifically, the adversarialloss metric may be based on a comparison between the ground-truth targetimage and the predicted target image. The adversarial loss metricindicates a likelihood and/or probability that the predicted targetimage is a synthetic image.

More particularly, a loss network, such as but not limited to lossnetwork 180 of FIG. 1B, that implements an adversarial loss model, suchas but not limited to adversarial loss model 182, may be adversariallytrained to discriminate between synthetic images and natural images.

At block 876, a feature loss metric based on a feature loss model (orfunction) is determined. More specifically, the feature loss metric maybe based on the comparison between the ground-truth target image and thepredicted target image. The feature loss metric indicates a perceptualloss of features that are included in the ground-truth target image, butnot included in the predicted target image.

More particularly, a loss network, such as but not limited to lossnetwork 180 of FIG. 1B, that implements a feature loss model, such asbut not limited to feature loss model 184, may be trained recognizeand/or detect features in images. More particularly, the convolutionallayers in the loss network may be employed to detect features in each ofthe ground-truth target imaged and the predicted target image. Thefeature loss model detects the loss of object features included in theground-truth target image but not included in the predicted targetimage.

At block 878, a pixel loss metric based on a pixel loss model (orfunction) is determined. More specifically, the pixel loss metric may bebased on the comparison between the ground-truth target image and thepredicted target image. The feature loss metric indicates a pixel-wisedifference between the ground-truth target image and the predictedtarget image. In some embodiments, the feature loss metric indicates apixel-wise difference between a gradient of the ground-truth targetimage and a gradient of the predicted target image.

At block 880, ICM is updated based on a combination of the adversarialloss metric, the feature loss metric, and the pixel loss metric. Thecombination of the loss metric may include a weighted (via one or morehyperparameters) linear or nonlinear combination of the adversarial lossmetric, the feature loss metric, and the pixel loss metric. Thecombination may be a combination of various distances between theground-truth target image and the predicted target image. The variousdistances may include Euclidean distances, Manhattan distances, or thelike. The distances may include pixel-wise distances (or differences).In at least one embodiment, the pixel-wise distances may includepixel-wise distances in the gradients of the two images. The combinationmay be an overall loss function or loss metric. Thus, the overall lossmetric include a linear/nonlinear combination of the adversarial lossmetric, the feature loss metric, and the pixel loss metric. The overallloss metric may be back propagated.

At block 880, the ICM is updated based on the back propagated overallloss metric. Updating the ICM may include updating and/or adjusting theweights of the ICM. Various embodiments of gradient descent, gradientascent, or other methods for adjusting the weights of a machine-learningnetwork may be employed to update the ICM. In various embodiments, theICM is updated to minimize the overall loss metric

At decision block 882, it is determined whether to select other trainingviewpoints. For instance, the ICM may be trained via other sourceviewpoints and/or other target viewpoints of the same 3D object. Ifother training source and/or target viewpoints are to be employed in thetraining of the ICM, process 860 returns to block 866 to select othertraining viewpoint parameters. Otherwise, process 860 flows to decisionblock 886.

At decision block 884, it is determined whether to select another 3Dmodel. For instance, another 3D model of another object type may be usedto further train the ICM. If another 3D model is to be selected, process860 returns to block 864. Otherwise process 860 may terminate and/orreturn a calling process.

Illustrative Computing Device

Having described embodiments of the present invention, an exampleoperating environment in which embodiments of the present invention maybe implemented is described below in order to provide a general contextfor various aspects of the present invention. Referring to FIG. 9, anillustrative operating environment for implementing embodiments of thepresent invention is shown and designated generally as computing device900. Computing device 900 is but one example of a suitable computingenvironment and is not intended to suggest any limitation as to thescope of use or functionality of the invention. Neither should thecomputing device 900 be interpreted as having any dependency orrequirement relating to any one or combination of componentsillustrated.

Embodiments of the invention may be described in the general context ofcomputer code or machine-useable instructions, includingcomputer-executable instructions such as program modules, being executedby a computer or other machine, such as a smartphone or other handhelddevice. Generally, program modules, or engines, including routines,programs, objects, components, data structures, etc., refer to code thatperform particular tasks or implement particular abstract data types.Embodiments of the invention may be practiced in a variety of systemconfigurations, including hand-held devices, consumer electronics,general-purpose computers, more specialized computing devices, etc.Embodiments of the invention may also be practiced in distributedcomputing environments where tasks are performed by remote-processingdevices that are linked through a communications network.

With reference to FIG. 9, computing device 900 includes a bus 910 thatdirectly or indirectly couples the following devices: memory 912, one ormore processors 914, one or more presentation components 916,input/output ports 918, input/output components 920, and an illustrativepower supply 922. Bus 910 represents what may be one or more busses(such as an address bus, data bus, or combination thereof). Although thevarious blocks of FIG. 9 are shown with clearly delineated lines for thesake of clarity, in reality, such delineations are not so clear andthese lines may overlap. For example, one may consider a presentationcomponent such as a display device to be an I/O component, as well.Also, processors generally have memory in the form of cache. Werecognize that such is the nature of the art, and reiterate that thediagram of FIG. 9 is merely illustrative of an example computing devicethat can be used in connection with one or more embodiments of thepresent disclosure. Distinction is not made between such categories as“workstation,” “server,” “laptop,” “hand-held device,” etc., as all arecontemplated within the scope of FIG. 9 and reference to “computingdevice.”

Computing device 900 typically includes a variety of computer-readablemedia. Computer-readable media can be any available media that can beaccessed by computing device 900 and includes both volatile andnonvolatile media, removable and non-removable media. By way of example,and not limitation, computer-readable media may comprise computerstorage media and communication media.

Computer storage media include volatile and nonvolatile, removable andnon-removable media implemented in any method or technology for storageof information such as computer-readable instructions, data structures,program modules or other data. Computer storage media includes, but isnot limited to, RAM, ROM, EEPROM, flash memory or other memorytechnology, CD-ROM, digital versatile disks (DVD) or other optical diskstorage, magnetic cassettes, magnetic tape, magnetic disk storage orother magnetic storage devices, or any other medium which can be used tostore the desired information and which can be accessed by computingdevice 900. Computer storage media excludes signals per se.

Communication media typically embodies computer-readable instructions,data structures, program modules or other data in a modulated datasignal such as a carrier wave or other transport mechanism and includesany information delivery media. The term “modulated data signal” means asignal that has one or more of its characteristics set or changed insuch a manner as to encode information in the signal. By way of example,and not limitation, communication media includes wired media such as awired network or direct-wired connection, and wireless media such asacoustic, RF, infrared and other wireless media. Combinations of any ofthe above should also be included within the scope of computer-readablemedia.

Memory 912 includes computer storage media in the form of volatileand/or nonvolatile memory. Memory 912 may be non-transitory memory. Asdepicted, memory 912 includes instructions 924. Instructions 924, whenexecuted by processor(s) 914 are configured to cause the computingdevice to perform any of the operations described herein, in referenceto the above discussed figures, or to implement any program modulesdescribed herein. The memory may be removable, non-removable, or acombination thereof Illustrative hardware devices include solid-statememory, hard drives, optical-disc drives, etc. Computing device 900includes one or more processors that read data from various entitiessuch as memory 912 or I/O components 920. Presentation component(s) 916present data indications to a user or other device. Illustrativepresentation components include a display device, speaker, printingcomponent, vibrating component, etc.

I/O ports 918 allow computing device 900 to be logically coupled toother devices including I/O components 920, some of which may be builtin. Illustrative components include a microphone, joystick, game pad,satellite dish, scanner, printer, wireless device, etc.

Embodiments presented herein have been described in relation toparticular embodiments which are intended in all respects to beillustrative rather than restrictive. Alternative embodiments willbecome apparent to those of ordinary skill in the art to which thepresent disclosure pertains without departing from its scope.

From the foregoing, it will be seen that this disclosure in one welladapted to attain all the ends and objects hereinabove set forthtogether with other advantages which are obvious and which are inherentto the structure.

It will be understood that certain features and sub-combinations are ofutility and may be employed without reference to other features orsub-combinations. This is contemplated by and is within the scope of theclaims.

In the preceding detailed description, reference is made to theaccompanying drawings which form a part hereof wherein like numeralsdesignate like parts throughout, and in which is shown, by way ofillustration, embodiments that may be practiced. It is to be understoodthat other embodiments may be utilized and structural or logical changesmay be made without departing from the scope of the present disclosure.Therefore, the preceding detailed description is not to be taken in alimiting sense, and the scope of embodiments is defined by the appendedclaims and their equivalents.

Various aspects of the illustrative embodiments have been describedusing terms commonly employed by those skilled in the art to convey thesubstance of their work to others skilled in the art. However, it willbe apparent to those skilled in the art that alternate embodiments maybe practiced with only some of the described aspects. For purposes ofexplanation, specific numbers, materials, and configurations are setforth in order to provide a thorough understanding of the illustrativeembodiments. However, it will be apparent to one skilled in the art thatalternate embodiments may be practiced without the specific details. Inother instances, well-known features have been omitted or simplified inorder not to obscure the illustrative embodiments.

Various operations have been described as multiple discrete operations,in turn, in a manner that is most helpful in understanding theillustrative embodiments; however, the order of description should notbe construed as to imply that these operations are necessarily orderdependent. In particular, these operations need not be performed in theorder of presentation. Further, descriptions of operations as separateoperations should not be construed as requiring that the operations benecessarily performed independently and/or by separate entities.Descriptions of entities and/or modules as separate modules shouldlikewise not be construed as requiring that the modules be separateand/or perform separate operations. In various embodiments, illustratedand/or described operations, entities, data, and/or modules may bemerged, broken into further sub-parts, and/or omitted.

The phrase “in one embodiment” or “in an embodiment” is used repeatedly.The phrase generally does not refer to the same embodiment; however, itmay. The terms “comprising,” “having,” and “including” are synonymous,unless the context dictates otherwise. The phrase “A/B” means “A or B.”The phrase “A and/or B” means “(A), (B), or (A and B).” The phrase “atleast one of A, B and C” means “(A), (B), (C), (A and B), (A and C), (Band C) or (A, B and C).”

What is claimed is:
 1. A computer-readable storage medium havinginstructions stored thereon, which, when executed by a processor of acomputing device cause the computing device to perform actionscomprising: receiving a source image that includes a first view of anobject from a first viewpoint and includes a first portion of theobject; generating a target image that includes a second view of theobject from a second viewpoint, wherein the second view includes atleast a sub-portion of the first portion of the object and a secondportion of the object occluded in the first view, the second portionbeing predicted using an image completion model; and providing thetarget image.
 2. The one or more computer-readable storage media ofclaim 1, generating an intermediate image that includes an intermediateview of the object from the second viewpoint, wherein the intermediateimage includes a first region corresponding to the first portion of theobject and a second region corresponding to the second portion of theobject occluded in the first view; and updating the second region of theintermediate image corresponding to the second portion of the object toinclude the prediction of the second portion of the object.
 3. The oneor more computer-readable storage media of claim 2 generating a flowfield that maps a region of the source image corresponding to the firstportion of the object to the first region of the intermediate imagebased on a rotational transformation from the first viewpoint to thesecond viewpoint; determining a pixel value for each of a plurality ofpixels included in the first region of the intermediate image; andgenerating the intermediate image further based on the pixel value foreach of the plurality of pixels included in the first region of theintermediate image.
 4. The one or more computer-readable storage mediaof claim 3, wherein the pixel value for each of the plurality of pixelsis based on the flow field, a sampling kernel, and a portion of datathat corresponds to the first portion of the object.
 5. The one or morecomputer-readable storage media of claim 2, wherein generating theintermediate image is based on a geometric flow model that determines arotation of the object about an axis that includes a component within aplane of two-dimensional (2D) data.
 6. The one or more computer-readablestorage media of claim 2, further comprising: employing a geometric flowfield to determine the first region of the first view of the object,wherein the first region of the first view includes the first portion ofthe object; employing the geometric flow model to generate a flow fieldthat maps the first region of the first view of the target to the firstregion of the second view of the target; and generating the rotation ofthe first portion of the object based on the flow field, a samplingkernel, and a portion of the 2D data that corresponds to the firstportion of the first view.
 7. The one or more computer-readable storagemedia of claim 1, generating a background map based on an intersectionof a foreground region of the source image that corresponds to theobject and a foreground region of an intermediate image that correspondsto the object, wherein the intermediate image includes an intermediateview of the object from the second viewpoint; determining a backgroundregion of the intermediate image based on the background map; anddetermining a pixel value for each of a plurality of pixels included inthe background region of the intermediate image based on a backgroundregion of the source image that is a complement of the foreground regionof the source image.
 8. The one or more computer-readable storage mediaof claim 1, further comprising training the image completion model, thetraining comprising: providing an incomplete version of a first image,wherein the first image is a two-dimensional (2D) image based on athree-dimensional (3D) training data set; generating a predicted versionof the first image based on the image completion model and theincomplete version of the first image; and updating the image completionmodel based on an adversarial loss metric.
 9. The one or morecomputer-readable storage media of claim 1, the training furthercomprising: providing an incomplete version of a first image, whereinthe first image is a two-dimensional (2D) image based on athree-dimensional (3D) training data set; generating a predicted versionof the first image based on the image completion model and theincomplete version of the first image; determining a feature loss metricbased on a comparison between the predicted version of the first imageand the first image; and updating the image completion model based onthe feature loss metric.
 10. A method for generating views of an object,comprising: determining a new region of a new view of an object thatincludes a new portion of the object, the new region based on arotational transformation applied to two-dimensional (2D) data;generating a prediction of the new portion of the object; and providinga target image that includes the new view of the object, wherein the newregion of the new view includes the prediction of the new portion of theobject.
 11. The method of claim 10, further comprising: determining ainitial region of the new view of the object, wherein the initial regionincludes an initial portion of the object that is disoccluded in each ofthe initial view and the new view of the object; generating a rotationof the initial portion of the object, wherein the rotation includes avisual representation of the rotational transformation applied to aportion of the 2D data corresponding to the initial portion of theobject included in the initial view of the object; and providing the newview of the object, wherein the initial region of the new view includesthe rotation of the initial portion of the object.
 12. The method ofclaim 10, further comprising: determining an initial region of theinitial view of the object that includes the initial portion of theobject; generating a flow field that maps the initial region of theinitial view of the target image to the initial region of the new viewof the target image; and generating the rotation of the initial portionof the object based on the flow field, a sampling kernel, and a portionof the 2D data that corresponds to the initial portion of the initialview.
 13. The method of claim 10, further comprising: generating avisibility map based on the rotational transformation applied to the 2Ddata; and generating an intermediate view of the object, theintermediate view of the object from the new viewpoint, wherein the newregion of the new view of the object is masked from the intermediateview based on the visibility map.
 14. The method of claim 10, furthercomprising: generating three-dimensional (3D) coordinates for the objectbased on the 2D data; determining a background region of the initialview of the object based on a background mask for the object and the 2Ddata, wherein the background mask is generated for the object based onthe 3D coordinates for the object; generating a background region of thenew view of the object based on the background region of the initialview and the background mask for the object; and including thebackground region of the new view in the provided new view of theobject.
 15. The method of claim 10, further comprising: training theimage completion model, the training comprising: providing an incompleteversion of a first image, wherein the first image is a two-dimensional(2D) image based on a three-dimensional (3D) training data set;generating a predicted version of the first image based on the imagecompletion model and the incomplete version of the first image; andupdating the image completion model based on the adversarial lossmetric.
 16. The method of claim 10, further comprising: training theimage completion model, the training comprising: providing an incompleteversion of a first image, wherein the first image is a 2D image based onthe 3D training data set; generating a predicted version of the firstimage based on the image completion model and the incomplete version ofthe first image; determining a feature loss metric based on a comparisonbetween the predicted version of the first image and the first image;and updating the image completion model based on the feature lossmetric.
 17. The method of claim 10, wherein the image completion modelis trained with a feature loss metric in combination with an adversarialloss metric, wherein the adversarial loss metric discriminates betweensynthetic images and natural images and the feature loss metricdiscriminates between physical features included in a plurality of image18. A computing system for providing views of an object, comprising:means for generating an image completion model based on a 3D trainingdataset and a geometric flow model; means for generating a predictedimage of a disoccluded portion of a 3D object depicted in atwo-dimension (2D) image, wherein the predicted image is generated usingthe image completion model and a generated intermediate view; and meansfor generating a target image that includes the second view of the 3Dobject, wherein the target image includes the predicted image.
 19. Thecomputing system of claim 18, further comprising: means for training thegeometric flow model.
 20. The computing system of claim 18, furthercomprising: means for providing the target image to a user.